Everton striker Dominic Calvert-Lewin was controversially sent off but the 10-man Toffees held on to force an FA Cup third-round replay with Crystal Palace.
Calvert-Lewin was shown a straight red card in the 79th minute after on-field referee Chris Kavanagh had been advised to review the incident on a pitchside monitor after an intervention from Video Assistant Referee Michael Salisbury.
The England forward had his studs up as he slid in to win the ball in a challenge on Nathaniel Clyne and clipped the defender’s shin, although contact was minimal.
Everton fans booed the decision when the incident was replayed on a big screen at Selhurst Park, with Toffees boss Sean Dyche also shaking his head, unhappy at the verdict.
Calvert-Lewin, now without a goal in 12 matches, had earlier had one of the few clear-cut chances but could only shoot tamely at home goalkeeper Dean Henderson.
Jefferson Lerma fired just over from 20 yards for the Eagles, but Palace could not make their extra man advantage count.
Everton also suffered what looked to be a serious injury to winger Dwight McNeil, who was carried off on a stretcher with a leg injury late on.
Draw a fair result as the two sides have to do it again
Eberechi Eze nearly won it for the hosts in the eighth minute of nine added on at the end, but Everton goalkeeper Joao Virginia did well to push the strike around the post.
Palace had gained a 3-1 Premier League win over Brentford on 30 December to end an eight-game run without a victory, but were without the injured Michael Olise, who hurt his hamstring after scoring twice in that match.
Striker Jordan Ayew was also unavailable as he was with the Ghana squad before the Africa Cup of Nations, which runs from 13 January to 11 February.
Brazilian winger Matheus Franca, 19, was handed his first start since his move from Flamengo in August in a £17m deal that could rise to £26m.
Franca, playing on the right wing, produced one of the best moments of the first half with a purposeful run, before James Tarkowski fouled him just outside the penalty area. Eze, though, fired the free-kick over.
Elsewhere, Jeffrey Schlupp had a low strike saved and Lerma shot over from 20 yards.
But a draw was a fair outcome as both sides had three attempts on target and seven corners apiece.
Everton, now without a win in five matches in all competitions, went close when Arnaut Danjuma had an attempt deflected into the side-netting and also forced Henderson into a good save.
Amadou Onana also headed over when well placed, but neither side could score and will have to do it again at Goodison Park later this month.
Palace and Everton, 14th and 17th respectively in the Premier League table, will both be in the fourth-round draw, which takes place at 19:50 GMT on Monday, 8 January before Wigan Athletic host Manchester United.
Player of the match
ColemanSéamus Coleman
Crystal Palace
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Squad number30Player nameHenderson
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Squad number10Player nameEze
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Squad number11Player nameMatheus França
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Squad number16Player nameAndersen
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Squad number17Player nameClyne
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Squad number6Player nameGuéhi
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Squad number3Player nameMitchell
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Squad number15Player nameSchlupp
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Squad number14Player nameMateta
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Squad number26Player nameRichards
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Squad number19Player nameHughes
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Squad number8Player nameLerma
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Squad number29Player nameAhamada
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Squad number52Player nameOzoh
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Squad number22Player nameÉdouard
Everton
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Squad number23Player nameColeman
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Squad number12Player nameJoão Virgínia
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Squad number32Player nameBranthwaite
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Squad number10Player nameDanjuma
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Squad number7Player nameMcNeil
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Squad number19Player nameMykolenko
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Squad number37Player nameGarner
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Squad number8Player nameOnana
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Squad number6Player nameTarkowski
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Squad number11Player nameHarrison
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Squad number14Player nameBeto
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Squad number21Player nameAndré Gomes
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Squad number9Player nameCalvert-Lewin
Line-ups
Crystal Palace
Formation 4-2-3-1
- 30Henderson
- 17ClyneSubstituted forOzohat 85′minutes
- 16Andersen
- 6Guéhi
- 3Mitchell
- 26Richards
- 8LermaSubstituted forÉdouardat 84′minutes
- 11França de OliveiraSubstituted forAhamadaat 71′minutes
- 10EzeBooked at 13mins
- 15SchluppSubstituted forHughesat 71′minutes
- 14MatetaBooked at 87mins
Substitutes
- 5Tomkins
- 19Hughes
- 22Édouard
- 23Ebiowei
- 29Ahamada
- 31Matthews
- 44Riedewald
- 45Adaramola
- 52Ozoh
Everton
Formation 4-2-3-1
- 12Neves Virgínia
- 23Coleman
- 6Tarkowski
- 32Branthwaite
- 19Mykolenko
- 8Onana
- 37Garner
- 7McNeilSubstituted forAndré Gomesat 89′minutes
- 11Harrison
- 10DanjumaSubstituted forGomes Betuncalat 80′minutes
- 9Calvert-LewinBooked at 79mins
Substitutes
- 1Pickford
- 2Patterson
- 5Keane
- 14Gomes Betuncal
- 21André Gomes
- 22Godfrey
- 28Ramalho Chermiti
- 58Hunt
- 61Dobbin
- Referee:
- Chris Kavanagh
- Attendance:
- 24,489
Live Text
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Match ends, Crystal Palace 0, Everton 0.
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Second Half ends, Crystal Palace 0, Everton 0.
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Tyrick Mitchell (Crystal Palace) wins a free kick in the defensive half.
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Foul by James Garner (Everton).
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Corner, Crystal Palace. Conceded by João Virgínia.
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Attempt saved. Eberechi Eze (Crystal Palace) right footed shot from outside the box is saved in the bottom right corner. Assisted by Odsonne Édouard.
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Corner, Crystal Palace. Conceded by Vitaliy Mykolenko.
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Corner, Crystal Palace. Conceded by James Garner.
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Eberechi Eze (Crystal Palace) wins a free kick in the attacking half.
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Foul by André Gomes (Everton).
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Attempt missed. Jack Harrison (Everton) right footed shot from the centre of the box is too high following a set piece situation.
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Substitution, Everton. André Gomes replaces Dwight McNeil because of an injury.
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Beto (Everton) wins a free kick in the defensive half.
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Foul by Will Hughes (Crystal Palace).
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Jean-Philippe Mateta (Crystal Palace) is shown the yellow card.
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Attempt blocked. Jean-Philippe Mateta (Crystal Palace) right footed shot from the left side of the six yard box is blocked.
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Corner, Crystal Palace. Conceded by James Tarkowski.
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Attempt blocked. Eberechi Eze (Crystal Palace) left footed shot from the left side of the box is blocked. Assisted by Joachim Andersen.
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Substitution, Crystal Palace. David Ozoh replaces Nathaniel Clyne.
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Substitution, Crystal Palace. Odsonne Édouard replaces Jefferson Lerma.